630
PAUL DELAHAY
REVERSIBILITY AND IRREVERSIBILITY OF ELECTRODE REACTIONS IN OSCILLOGRAPHIC POLAROGRAPHY
THEV-4LIDITY O F
THE m7AVE
HEIGHTEQU.4TION
PAUL DELAHAY'
Department of Chemistry, University of Oregon, Eugene, Oregon Receiaed July 86, 1949
The theory of the diffusion process taking place in oscillographicpolarography has been discussed in two recent papers by Randles (7) and by Sevcik (8). Randles derived the following expression for the height of an oscillographic wave corresponding to a reversible electrode reaction
in which I = the height of the oscillographic wave in amperes, 8 = the faraday, = the number of electrons involved in the reaction, y = related to the radius T of the mercury drop by the relation Id = y ~ , T = the time of the drop life at which the peak current occurs, v = the rate of potential change in volts per second, D = the diffusion coefficient of the substance reacting at the dropping mercury electrode in square centimeters per second, and C = the concentration of the substance reacting at the electrode in moles per liter. Equation 1 can be transformed into a more convenient form in the following manner. By expressing the weight of the mercury drop as a function of m, the rate of flow of mercury, one obtains
4
3?ry~6= mr
S being the density of mercury. Thus y = 0.01764m
(3)
m being expressed in grams per second. Substituting this value of y in formula 1 one obtains, after grouping the numerical constants, I = 2,344n3/2 ,2'a T z / 3v112 D1I2 C (4) in which the following units are used: I in microamperes, m in milligrams per second, T in seconds, v in volts per second, D in square centimeters per second, C in millimoles per liter. 1 Present address : Department of Chemistry, Louisiana State University, Baton Rouge 3, Louisiana.
ELECTRODE REACTIONS I N OSCILLOGRAPHIC POLhROGRAPHY
63 1
For practical purposes, the factor r of formula 4 may be taken as equal to the drop time when only the nave corresponding to the maximal area of the mercury drop is taken into consideration, a fairly large number of waves being recorded during the life of a single drop. The current corresponding to the maximal area of the drop has been called “maximal peak current” by the author of the present paper. On the other hand, Sevcik (8) has derived the following equation for the height of an oscillographicwave written with the notations of formula 1:
in which R and T have their usual significance,A is the area of the mercury drop at the time of the drop life at which the peak current occurs, expressed in square centimeters, a,nd C’ is expressed in moles per milliliter. Expressing the area A as a function of m and T one obtains
=
0.851jm2’3 T 2 ’ 3
(7)
m being expressed in grams per second.
Substituting this value of A in formula 5 and grouping the numerical constants one obtains an equation identical with formula 4 except for the numerical constant, which becomes 1,852. In evaluating the reliability of either result it should be pointed out that Randles determined the height of a few oscillographic waves and found them in good agreement with the values calculated by application of his formula. On the other hand, Sevcik limited his experimental work to the verification of the proportionality between the wave height and the factors v and C. Moreover, the results obtained in the present paper tend to confirm Randles’ equation rather than Sevcik’s. Therefore, all calculations described in the present paper have been carried out according to Randles’ equation (formula 4). Equation 4 has been derived by assuming that the electrode reaction is reversible. The correctness of equation 4 was verified experimentally by Randles for rates of potential change not exceeding 1 volt per second. It is the purpose of the present paper to extend this verification to higher rates of potential change and also to examine the case of irreversible electrode reactions. The experimental arrangement has been previously described (4) and does not need any further comment. All results correspond to measurements carried out a t 25°C.
m ASD T According to formula 4 the maximal peak current I is proportional to the quantity (m.) 3. Since the product mr is independent of the pressure on the dropping electrode (5, p. i o ) within a few per cent, the maximal peak current DEPENDENCE OF THE MAXIMAL PEAK CURRENT ON THE FACTORS
632
PAUL DELAH.%Y
should be practically independent of that pressure. We found that this mas indeed the case for the reduction of zinc ion (3). However, an extensive study 2OOr
I
I
500
700
I
I50
100
300
900
FIG.1. Variation of the maximal peak current with the mercury head. h = head of mercury (in mm.); no correction for the back pressure. I = maximal peak current (in per cent). Curve I . . ,
. , ... .. ,i 1
SbC13(10-3 mole/liter) in H?SOa (0.5 mole/liter); f = 12 sw-eeps/sec.; v = 24.9 v./sec.; I l o o= 494 microamp.
I
'
Curve 11. Curve I11
~
~
Pb(K03)2(10-3 mole/liter) in KS03 (0.5 mole/liter); f = 20 sweeps/ sec.; = 68.1 v./sec.; I l o o = 343 microamp. CdSOa (10-3 mole/liter) in KCI (1 mole/liter); f = 12 sweeps/sec.; v = 29.9 v./sec.; Ilo0= 239 microamp.
1
I
1
Curve IV. . , , . , , Curve V.
,
TliY03 (10-3 mole/liter) in K X 0 3 (0.5 mole/liter); f = 12 sweeps/sec. v = 34.8 v./sec.; I M O= 189 microamp.
1 KIO~ ~
1
v
=
(10-3 mole/liter) i n H,SO, (0.5mole/liter); 68.1 v./sec.; Iloo = 383 microamp.
f = 20 sweeps/sec.;
NiSOa (10-3 mole/liter) in (CHajrSBr(0.1 mole/literj;f = 20 sweeps/ sec.; ti = 44.0 v./sec.; IlOo= 25.2 microamp.
Curve V I . ~
Curve VII. Curve VIII., . , , , . ,
KI03 (10-3 mole/liter) in KaOH (0.1 mole/liter) ;f = 20 sweeps/liter; u = 68.1 v./sec.; I100 = 179 microamp.
,
~
1
HC1 (10-3 mole/liter) in LiCl (0.5 mole/liter); f = 20 sweeps/sec.; u = 51.1 v./sec.; I l ~ o= 63.5microamp.
has shown that, in general, there is a dependence of the maximal peak current on the head of mercury. The maximal peak current either increases or decreases when the head of mercury is increased, although an increase in the current is more frequently observed.
633
ELECTRODE REACTIOSS I N OSCILLOGRAPHIC POLAROGRAPHY
The variations of t'he maximal peak current with the head of mercury are rather small for electrode reactions which are known to occur reversibly or almost reversibly. This is the case for the reduction of cadmium and thallous ions (curves I11 and I V of figure 1). For irreversible electrode reactions the variations of the maximal peak current with the head of mercury are very large (figure l). When the overvoltage required for the reduction of a substance changes with the nature of the supporting electrolyte, it is observed that the reaction occurring with the lowest overvoltage also s h o w the smallest variation of the maximal peak current with the head of mercury. This conclusion is verified in figure 1 for the reduction of iodate ion, which is less irreversible in acid (curve V) than in alkaline solution (curve VII) ( 5 , p. 320). In the case of an irreversible reaction it is also observed that the variations of the maximal peak current with the mercury head increase in amplitude with the rate of potential change (table 1). TABLE 1 V a r i a t i o n of the m a z i m a l peak current with the head of mercury in the case of a 10-3 molar cobaltous nitrate solution in 1 molar potassium chloride
1
HE.4D OF M R C C R S
1 8';
U X I S L 4 L PEAK CURRENT EXPRESSED IX PEE CEYI OF TI% VALUE FOR A OF 375 XM.
' f = 15 sweeprlsec. f = 30 sweepsisec. f = 60 swecps/sec. = 2 0 . 5 v./sec. ~ ~ v = ~ 3 . 3 r . i s : c . o=96.5v./rec. v=195v./rec. = 45.7microamp., I l o b 51.2 microamp., It00 = 60.8 microamp.1 I100 = 69.5microam~.
i = 7.5 sweepslsec.
-
1 Iioo mm
3i5 519 669 841 -~
~
i
BEAD OF MERCUPY
per ccnt
100 122 152 183
1 I
,
~
per cent
100 124 150 189
per
ILnl
100 129 158 202
~~
per ccnt
100 133 164 209
The dependence of the maximal peak current on the head of mercury in the case of an irreversible electrode reaction implies that equation 4 is no longer applicable. I t might be thought that the experimental results could be interpreted by a formula similar to equation 4, in Tvhich the factors m and r would be affected with arbitrary exponents x and y. These exponents could be calculated from the results of a set of three experiments carried out with three different values of the head of mercury. Such calculations have been carried out for some of the reactions mentioned in figure 1, but it was found that the exponents x and y vary widely with the head of mercury. Therefore it is not possible to extend the application of formula 4 to irreversible electrode reactions by merely changing the value of the exponents of the factors m and r. Because of the dependence of the maximal peak current on the head of mercury, maximal peak currents recorded with different dropping elertrodes cannot be correlated with one another in the case of an irreversible electrode reaction. On the other hand, in the case of a reversible electrode reaction the results obtained with different values of m and T can be compared with one another by application of formula 4. However, before doing so one should verify that the maximal peak current actually does not depend on the head of mercury.
634
PAUL DELAHAY
The study of the variations of the maximal peak current with the head of mercury gives us a very simple method of determining whether an electrode reaction occurs reversibly or irreversibly. I n the case of a reversible electrode process the maximal peak current will practically not depend on the mercury head, while in the case of an irreversible electrode reaction the maximal peak current will change appreciably with the value of the head of mercury.
0
3
6
9
1215
FIG.2 FIG. 3 FIG.2. Variation of the maximal peak current with the rate of potential change in the case of a “reversible” electrode reaction. u = rate of potential change (v./sec.); Z maximal peak current (microamp.). TIN08 (10-8 mole/liter) in KNO: (0.5mole/liter); m = 1.41 mg./sec.; T = 4.40 sec. Curve I, calculated by application of formula 4, I 35.4&. Curve 11, experimental results. FIG.3. Variation of the maximal peak current with the rate of potential change in the case of a “reversible” electrode reaction. Pb(NOa)2(10-smole/liter) in KNOa (0.5 mole/ liter); m = 1.41 mg./sec.; T = 4.00 sec. Curve I, calculated by application of formula 4, Z = 66.G Curve . 11, experimental results.
-
DEPENDENCE O F THE MAXIMAL PEAK CURREKT ON T H E RATE OF POTENTIAL CHANQE
Experimental results According to formula 4 the maximal peak current is proportional to the square root of the rate of potential change in the case of a reversible electrode reaction. This relationship has been verified experimentally and a few typical results are shown in figures 2 4 . I n these diagrams the dotted line corresponds to the maximal peak current as calculated by application of formula 4;the solid line corresponds to the experimental results. The values of the diffusion coefficient used in this calculation are those corresponding to infinite dilution (5, p. 45). For the T1+ solution (figure 2) equation 4 is essentially correct over the investigated range of rates of potential change.
ELECTRODE RE.4CTIOKS IK OSCILLOGRAPHIC POLAROGRAPHY
635
On the other hand, for Pb++ and Cd++ solutions (figures 3 4 ) one observes a marked departure from the calculated values. It could be objected that a calculation based on the value of the diffusion coefficient at infinite dilution certainly yields too high a value for the maximal peak current. This circumstance could account partially for the discrepancy observed between the calculated and experimental results. However, the ratio of the experimental value of the maxima1 peak current to the calculated value decreases as the rate of potential change increases (table 2), and this effect can not be explained by any error in the value
0
3
6
9
FIG.4
1 2 1 5 FIG.5
FIG.4 . Variation of the maximal peak current with the rate of potential change in the case of a “reversible” electrode reaction. CdSOa (10-3 mole/liter) in KC1 (1 mole/liter); 7n = 1.41 mg./sec.; T = 4.40 sec. Curve I, calculated by application of formula 4, I = 60 2&, Curve 11, experimental results. FIG.5 . Variation of the maximal peak current with the rate of potential change in the case of a n “irreversible” electrode reaction. HC1 (10-8 mole/liter) in LiCl (0.5 mole/liter) ; n = 1.41 mg./sec.; T = 2.40 sec. Curve I, calculated by applicationof formula 4, I = 51.3uy. Curve 11, experimental results.
of the diffusion coefficient. The reason underlying the existence of this effect will be given below. A few irreversible electrode reactions have also been investigated; the results are shown in figures 5-7. The experimental currents are much smaller than the calculated values (table 2). Therefore equation 4 is by no means applicable even at a rate of potential change of a few volts per second.
Interpretation of the diagram I = f(v”’) The diagram I = f(vi‘*) can be interpreted in a satisfactory manner by assuming that the rate of the electrode reaction is a factor controlling the strength of the maximal peak current in the case of an irreversible electrode reaction. This
636
PAUL DELAHAY
influence of the reaction rate is the more pronounced the higher the rate of potential change. Consequently, a curvature appears in the diagram I = f(v”*) and of the experimental current to the calculated value the ratio Iexgtl./Ioa,ed. (formula 4) decreases as v increases (table 2 ) . The magnitude of the rate effect depends on the nature of the electrode process.
0
3
6
9
1 2 1 5
0
3
6
9
1 2 1 5
FIG.6 F I G .7 FIG.6. Variation of the maximal peak current with the rate of potential change in the case of an “irreversible” electrode reaction. Curves I , 11: NiS04(10-3 mole/liter) in (CH3)4NBr(0.1 mole/liter); m = 2.17 mg./sec.; T = 1.80 sec. Curve I , calculated by application of formula 4, I = 4 3 . 4 ~Curve ~. 11, experimental results. Curves 111, I V : NiSO, (lOP mole/liter) in KCNS (0.5 mole/liter); m = 2.17 mg./sec.; T = 3.50 sec. Curve 111, calculated by application of formula 4, I = 6 7 . 7 ~Curve ~. IV, experimental results. FIG. 7. Variation of the maximal peak current with the rate of potential change in the caae of an “irreversible” electrode reaction. Curves I , 11: KIOI (10-3 mole/liter) in NaOH (0.1 mole/liter); m = 1.41 mg./sec.; T = 3.30 sec. Curve I , calculated by application of formula 4, I = 3 1 8 ~ sCurve . 11, experimental results. mole/liter) in HzSOl (0.5 mole/liter); m = 1.41 mg./sec.; T Curves 111, IV: KIOI = 4.00 sec. Curve 111, calculated by application of formula 4, I = 3 6 1 ~ s Curve . IV, experimental results.
For a reversible electrode reaction no rate effect should be observed, and formula 4 is applicable for any value of the rate of potential change. This is the case of the reduction of thallous ion (figure 2 ) . For an irreversible electrode reaction the rate effect will depend on the free energy of activation of the process involved. This dependence can be shown in a qualitative manner by considering the relation connecting the free energy of activation with the current density at an electrode on which the reaction is taking place. In the case for which the rate of the electrochemical process is the
ELECTRODE REACTIOSS I N OSCILLOGRAPHIC POLAROGRAPHY
63 7
TABLE 2 Calculated and exverimental maximal veak currents at different rates of potential chanqe
TKO3 Pb(NOj)? CdSOA HC1 NiS04 in (CH3)4Br NiSO4 in KCNS KIOI in NaOH KI03 in H&O1
Figure Figure I Figure Figure Figure Figure Figure Figure
2 3 1 5
6 6 7 7
!Jollr/rsc.
per cent
10.4 11.9 8.90 8.90 9.00 4.50 11.8 11.8
97.1 i0.4 82.3 29.3 16.9 12.9 11.8 18,1
Per cent
Lolls/sLc
138 110 168 168 120
ii!
223
~
~
94 7 60 3 54 6 10 7 5 95 2: 6: 8 97
only factor controlling the current, the following equation for the current density has been derived recently by Van Rysselberghe (9) :*
in which &.
= the current density in amperes per square centimeter, n = the number of electrons involved in the reaction, 8 = the Faraday, a = the activity of the substance reacting at the electrode, expressed in moles per liter, AF' = the free energy of activation of the process taking place at the electrode, expressed in calories, J.a = the electrical potential of the reacting species in solution, in volts , J.. = the electrical potential of the reacting species in its activation position closest to the electrode, in volts, and e , k , h,T, and R havz their usual significance. The term (J.. - 4.) appearing in relation 8 is not known exactly, hut it can he expressed in terms of the potential difference between the electrode and the solution by introducing the notion of transfer coefficient. However, these developments are not needed here. Formula 8 thus gives the maximum current density at which the electrode process is taking place for a given value of (+ha In oscillographic polarography there is concentration polarization at the dropping mercury electrode and the maximal peak current cannot be calculated by application of formula 8. Nevertheless, formula 8 shows that the maximal peak current depends on the free energy of activation of the electrode process and, furthermore, that the higher the free energy of activation the smaller the strength of the maximal peak current mill be, all other conditions being the same. The correctness of this statement can he proved experimentally by studying
* The reverse reaction is neglected
in relation 8
638
PAUL DELAHAY
the reduction of iodate ion in various media. It is known from ordinary polarography that the reduction of iodate ion involves a smaller free energy of activation in acid medium than in alkaline solution (5, p. 320). It follows from formula 8 that the maximal peak current of a potassium iodate solution should be larger in an acid supporting electrolyte than in an alkaline medium, all other conditions being the same. The results indicated on figure 7 and in table 2 show that this is indeed the case.3 The reduction of the nickel ion in various supporting electrolytes is similar to the case of the reduction of iodate ion. It is known from ordinary polarography that the reduction of the nickel ion in a potassium thiocyanate solution involves a smaller free energy of activation than in a potassium chloride solution (5, p. 281). As a result, the maximal peak current of a nickel ion solution in a thiocyanate medium is larger than in a potassium chloride solution, all other conditions being the same (figure 6, curves I1 and IV). APPLICATION T O T H E DETERMINATION OF T H E REVERSIBILITY O F AN ELECTRODE PROCESS
The comparison of the experimental diagram I = f(vl‘*) with the theoretical one aa calculated by application of formula 4 gives us a method of deciding whether an electrode reaction occurs reversibly or irre~ersibly.~ The shape of the diagram Z = f(u”*) ikiabo a criterion of reversibility, because a curvature in the diagram indicates the irreversibility of the electrode process. Figures 2 to 7 are examples of application of this method. Among these cases the reduction of cadmium ion is of special interest because this reaction is supposed to occur reversibly (5, p. 269) at the dropping mercury electrode, while the oscillographic method shows definitely that the reduction is actually slightly irreversible. This irreversibility does not appear in ordinary polarography, because it could be detected only by certain effects which are beyond the accuracy of measurement or calculation. On the other hand, this slight irreversibility appears in oscillographic polarography because of the very short duration of the wave re~ording.~ IMPLICATIONS FOR ANALYTICAL APPLICATIONS OF T H E OSCILLOGRAPHIC METHOD
From the discussion in the previous section it is obvious that any factor affecting the rate of the electrode reaction will modify the strength of the maximal peak current. If such a modification of the reduction rate is taking place 8 It should be pointed out that curves I1 and I V have not been recorded with the same drop time, although the difference between the drop times, which are respectively 3.30 and 4.00 sec., is not large enough to account for a wide difference between curves I1 and IV. 4 The value of the diffusion coefficient appearing in formula 4 can be easily determined by running an ordinary polarogram and by calculating D from the value of the diffusion current (IlkoviE equation). 6 This effect ehould not be confused with the “rate current” observed in ordinary polarography in some cams, for which the diffusion current is limited by the rate of transformation of one substance into another (1, 2, 6).
ELECTRODE REACTIONS I N OSCILLOGRAPHIC POLAROGRAPHY
639
when the experimenter is unaware of it, the maximal peak current may be seriously in error. Therefore, it is essential to work in conditions such that the rate of the electrode reaction is well defined. This condition brings about a difficulty which is not encountered in ordinary polarography. For example, the oscillographic determination of the iodate-ion concentration in an unbuffered supporting electrolyte Jyould not be very reliable, since a modification of the pH of the solution xould result in a variation of the maximal peak current, as we have seen previously. I t is therefore essential in the present case to record the iodate Tyave in a buffered medium. In ordinary polarography this vould not be necessary, since a sliglit variation in the pH of the supporting electrolyte would not appreciably affect the value of the diffusion coefficient of the iodate ion. SUMMARY
The equations obtained by Randles and by Sevcik for the height of an oscillographic polarogram have been recalled. After transformation these equations were found to be identical except for a difference in a numerical constant. Several of the factors appearing in the equation have been investigated experimentally. For a reversible electrode reaction Randles’ equation was found to be correct. For an irreversible electrode process the rate of the reaction is a controlling factor of the current and the experimental results cannot be predicted by Randles’ equation. The dependence of the ~ a v height e on the rate of the electrode reaction is interpreted in terms of the free energy of activation of the electrode process involved. Experimental implications of the reaction rate dependence are discussed. I t is concluded from the experimental data that some electrode processes which are usually considered as occurring reversibly, actually involve a small free energy of activation. This work is part of a research project entitled “Polarographic Study of Corrosion Phenomena” carried out at the University of Oregon under contract with the Office of Naval Research. The author is indebted to Professor Pierre Van Rysselberghe, Director of the project, for very helpful discussions on overvoltage theories as well as for the discussion of the contents of the present paper. REFERENCES (1) (2) (3) (41 (5)
BRDIEKA, R.: Collection Czechoslov. Chem. Commun. 12, 212 (1947). BRDIEKA, R . , AND WIESSER,K.: Collection Czechoslov. Chem. Commun. 12, 138 (1947). DELAHAY, P.: J. Phys. 8: Colloid Chem. 63, 1279 (1949). DELAHAY, P . : J. Phys. 8: Colloid Chem. 64, 402 (1950). KOLTHOFF,I. hf., A N D LISGANE,J. J.: Polarography. Interscience Publishers, Inc.,
(6) (7) (8) (9)
New York (1941). KOUTECKY, J., b S D BRDIEKA, R.: Collection Czechoslov. Chem. Commun. 12,337 (1947). RANDLES, J. E. B.:Trans. Faraday SOC.44. 327 (1948). SEVCIK,A.: Collection Caechoslov. Chem. Commun. 13, 349 (1948). VANRYSSELBERGHE, P.: J. Chem. Phys. 17 (December, 1949).
